We show that the strong correlation observed between the braking indices (n) and the slowing-down ages (Τ) of pulsars is inconsistent with counteralignment between their rotation and magnetic axes, but that the data on pulsars with positive braking indices is consistent with alignment. Alternatively, slowing-down noise can quantitatively account for the data on all pulsars except the Crab and the Vela, and so for the apparent|n| ∼ Τ² correlation observed for the older pulsars.

If the dwarf spheroidals are embedded in an extended cloud of dark matter then their density profiles can be reproduced by assuming a Maxwellian distribution of velocities for the constituent stars. The observed luminosity profiles of dwarf spheroidals imply densities for the dark matter in the range 10^-26 to 10^-25 g cm^-3, and mass-to-luminosity ratios which are typically an order of magnitude greater than those of globular clusters. Neutrinos of mass ∼ 10 eV and (v) ∼ 1000 km s^-1 can provide this requisite density for the background.

Extensive and meticulous observations of the rotation curves of galaxies show that they are either flat or gently going up, but rarely decreasing, at large galactocentric distances. Here we show that the gravitational potential which would lead to such rotation curves arises naturally when the visible matter modelled as a collisionless Maxwellian gas is embedded in a dark halo of collisionless particles with a much higher dispersion in velocities.

I review our understanding of the evolution of the spin periods of neutron stars in binary stellar systems, from their birth as fast, spin-powered pulsars, through their middle life as accretion-powered pulsars, upto their recycling or “rebirth” as spin-powered pulsars with relatively low magnetic fields and fast rotation. I discuss how the new-born neutron star is spun down by electromagnetic and “propeller” torques, until accretion of matter from the companion star begins, and the neutron star becomes an accretion-powered X-ray pulsar. Detailed observations of massive radio pulsar binaries like PSR 1259-63 will yield valuable information about this phase of initial spindown. I indicate how the spin of the neutron star then evolves under accretion torques during the subsequent phase as an accretion-powered pulsar. Finally, I describe how the neutron star is spun up to short periods again during the subsequent phase of recycling, with the accompanying reduction in the stellar magnetic field, the origins of which are still not completely understood.

I summarize X-ray diagnostic studies of cosmic star formation history in terms of evolutionary schemes for X-ray binary evolution in normal galaxies with evolving star formation. Deep X-ray imaging studies byChandra andXMM-Newton are now beginning to constrain both the X-ray luminosity evolution of galaxies and the logN- logS diagnostics of the X-ray background. I discuss these in the above context, summarizing current understanding and future prospects.